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PreprintCC BY 4.0arXiv

A nilpotent version of the first Kac conjecture

  • Lydia Gösmann
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Abstract

We derive a formula for the nilpotent Kac polynomial and define an explicit generalized Kac-Moody Lie algebra (by generators and relations) and conjecture that its graded dimensions recover the constant terms of the nilpotent Kac polynomial. We outline empirical evidence supporting the conjecture and prove it for two special classes of quivers: quivers without oriented cycles except loops and quivers with "negative enough" Euler form.

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Cite

BibTeXRIS
BibTeX
@misc{gosmann2026nilpotent,
  title = {{A nilpotent version of the first Kac conjecture}},
  author = {Lydia Gösmann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37207},
  eprint = {2610.37207},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37207},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A nilpotent version of the first Kac conjecture
AU  - Lydia Gösmann
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37207
UR  - https://arxiv.org/abs/2610.37207
AB  - We derive a formula for the nilpotent Kac polynomial and define an explicit generalized Kac-Moody Lie algebra (by generators and relations) and conjecture that its graded dimensions recover the constant terms of the nilpotent Kac polynomial. We outline empirical evidence supporting the conjecture and prove it for two special classes of quivers: quivers without oriented cycles except loops and quivers with "negative enough" Euler form.
ER  -